Pinpointing a disastrous limitation of Special Relativity and Proposing a new explanation for Light Speed’s constancy

: This paper pinpoints a severe infirmity of the Lorentz Transformation in the Special Theory of Relativity. Even if it were true, its ambit is very much limited. Out of infinite events happening in the universe, it covers only the events of detecting light signals at the spatial points lying on a straight line in the direction of the relative velocity between the two inertial frames. This paper points out that the slowing down of moving clocks is not a prediction of Lorentz Transformation and hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity. This paper concludes that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in narrow-scoped and unrealistic Lorentz Transformation.

Everyone's world is their perception. Any absolute reality beyond the perceptional realities of the observers seems to be beyond the cognitive limits of human capabilities.
But, fortunately for all human beings, though their perceived 'facts' may differ, the laws of Nature connecting one's perceived 'facts' are the same. A stone's trajectory dropped by a passenger in a moving train is a straight line for him, whereas it is a parabola for an observer standing on the platform. Both observers would agree that the same laws of Physics govern the physical realities perceived by them. The First Postulate of Special Relativity succinctly states this fact as follows; "The laws of nature have the same mathematical form in all inertial reference frames" [1]. Though the laws are the same, the scenarios of the same reality observed in different inertial frames need not be the same, as exemplified by the fact that the stone's trajectory is a straight line and a parabola in the train frame and the platform frame, respectively. This paper is a relook of Special Relativity in the Light of Perceptional Relativity, which means that the observers stationed in different inertial frames perceive the same reality differently. There is no absolute perception of that reality.
As there is no meaning for "distance" in an empty world, there is no meaning for "Time" in an eventless world. If the whole universe became frozen and static, Time would disappear. If a single change takes place at a point anywhere in the universe, that change is an "event". The human brain has an intrinsic faculty known as "Memory", and an event 'after' it has happened becomes a memory in the human brain.
The objects are real, and the "distance" between two objects is the relation intellectually constructed by the human brain. Similarly, the events are real; the "time interval" between two events is a relation intellectually built by the human brain with the aid of its memory faculty recording events that have happened and its rational faculty to anticipate events that may occur. Distances and time come into play only to quantify the relations among the objects and events. Hence, an event is more fundamental than time. Einstein's Special Relativity, instead of sticking to events, went astray by shifting the focus on the rulers and clocks used for measuring distances and times. Events are absolute in the sense that the observers do not deny their occurrences in all inertial frames notwithstanding their differing on where and when those events happened.

Section 2: Discussion
PART -I A serious limitation of Lorentz Transformation Equations

An Extract from Einstein's Original Paper
The following is an extract of a crucial part of Einstein's derivation of Lorentz Transformation Equations [2]:

"We now have to prove that any ray of light, measured in the moving system, is
propagated with the velocity c, if, as we have assumed, this is the case in the stationary

system; for we have not as yet furnished the proof that the principle of constancy of the velocity of light is compatible with the principle of relativity.
At the time t = τ = 0, when the origin of the coordinate system is common to the two systems, let a spherical wave be emitted therefrom, and propagated with the velocity c in system K.

If (x, y, z) be a point just attained by this wave, then
x 2 + y 2 + z 2 = c 2 t 2 .

The wave under consideration is therefore no less a spherical wave with velocity of
propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible. 5 " "Footnote: 5. The equations of Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x 2 + y 2 + z 2 = c 2 t 2 shall have as its consequence the second relation € 2 + ή 2 + ζ 2 = c 2 τ 2 ."

Lorentz Transformation from Lorentz Invariance
Firstly, as stated in the Footnote by Einstein, let us first deduce the equations of Lorentz transformation directly from the condition that in virtue of those equations the relation x 2 + y 2 + z 2 = c 2 t 2 shall have as its consequence the second relation € 2 + ή 2 + ζ 2 = c 2 τ 2 ." Let us begin with the following equations.
x' = a (xvt); (1) y' = y; and (1a) [For the sake of easy typing, we have used the notations x', y' and z' instead of €, ή and ζ, respectively. Similarly, we shall use t' instead of τ.] The factor a in Equation (1) is the Lorentz Factor commonly denoted as ᵞ in many textbooks on Relativity. When x' = x -at is the physical reality, the inclusion of a, the Lorentz Factor, in the first place, is only an artificial mathematical manipulation to make the two equations x' = xat and x = x' + at' identical even when t ≠ t' to account for the interchangeability of the frames demanded by the First Postulate of the Special Theory of Relativity. A mathematical consequence of such inclusion of an unrealistic factor is "Length Contraction", which is the shortening of the lengths measured by the observers of one inertial frame in the perspective of the observers in other frames.
x -x'/a = vt, from the perspective of the unprimed frame, and x/a -x' = vt' from the perspective of the unprimed frame which, in turn, led to "Time Dilation", which is the shortening of the time intervals measured by the observers of one inertial frame in the perspective of the observers in other frames x/c -x'/ac = vt/c, from the perspective of the unprimed frame, and x/ac -x'/c = vt'/c from the perspective of the unprimed frame when x = ct and x' = ct' tt'/a = vx/c 2 , from the perspective of the unprimed frame, and t/a -t' = vx'/c 2 from the perspective of the unprimed frame.

is clear that the equations must be linear on account of the properties of homogeneity
which we attribute to space and time." [2] Let us first agree with Einstein and take t' as a linear function in x and t.
[We shall later prove that t' is a linear function in x and t only for propagation of light along the direction of the relative velocity between the two frames.] 7 Taking t' to be a linear function in x and t where the values of the coefficients d and e have to be determined.

Proving the limitation of Lorentz Transformation
Now, we are going to prove in three different methods that Lorentz Invariance i.e., € 2 + ή 2 + ζ 2 -c 2 τ 2 = x 2 + y 2 + z 2 -c 2 t 2 is valid only when the direction of propagation of the ray of light is the same as the direction of the relative velocity between the two systems. In other words, if the direction of the relative velocity between the two systems is taken as X-axis, the equation holds good only in respect of the points lying on the X-axis and fails in respect of the points not lying on the X-axis. This means that Lorentz Transformation is valid only for ή = y = 0 and ζ = z = 0

FIRST METHOD
The following Pictures give an 'assumed' scenario of an event of detection of Light at a spatial point in the X-Y Plane that does Not lie on the X-Axis.
From the perspective of both S and S'.
x = ct cosθ (7) x' = ct' cos Ф (8) Substituting the above values of x in Lorentz Transformation Equations (5), we get Substituting the above values of x' in Lorentz Transformation Equations (5a), we get Substituting the value of x' from Equation (9) in Equation (9a),

SECOND METHOD
We may arrive at the above conclusion in another way also.
x' 2 + y' 2 + z' 2c 2 t' 2 = x 2 + y 2 +z 2ct 2 Since y' = y, z' = z, the above identity is reduced to The Detection of a Light Signal at a spatial point in X-Y plane (not on X-axis) from the perspective of the Frame S' The expression for t' can have a linear form if and only if y' = 0 i.e., the point of detection of Light Signal falls on X-axis

THIRD METHOD
We may arrive at the same conclusion that Lorentz Transformation is valid only when the direction of propagation of the ray of light is the same as the direction of the relative velocity between the two systems in a third way also.
For a pair of events whose space and time distances are measured by the observers in the frames S and S', let us define two values p and q as follows: p = x/t and q = x'/t' We shall derive Generalized Transformation Equations involving p and q so that that in our derived Equations, if we substitute both p and q with c we shall get the usual Lorentz Transformation Equations. In other words, p = q = c is a special case of Generalized Transformation Equations; and this special case is Lorentz

Transformation Equations
Let us consider two events. Let the first event be taken as the Origin Event and assigned the coordinates (0,0) by both frames.
Let the space difference and the time difference between the events under consideration be pt and t for the frame S respectively; and qt' and t' for the frame S' respectively.
The following figure depicts the scenario of the second event E from the perspective of the frame S, Transformation includes a factor, say a, to the RHS of the two equations with a view to the Event for S derive an expression for a so as to make the Equations (T1) and (T2) identical. This factor a (named ᵞ in many text books) is called Lorentz Factor.
With the inclusion of Lorentz Factor (a), the Equations (T1) and (T2) become When we rewrite the above Equations (T3) and (T4) in the following formats, The above Equations Using the two values p and q, which we have already defined, we can rewrite Equations (T3) and (T4) as follows: From Equations (T3c) and (T4c), The above Equation (T5) gives the general expression for Lorentz Factor (a).
For a particular case where p = q = ± c, Therefore, since Lorentz Transformation takes only the above particular value of Lorentz Factor a, it is applicable only to the pairs of events representing transmission of light with speed c in positive or negative direction and it cannot be applied to other pairs of events.
As regards the 'assumed' scenario of an event of detection of Light at a spatial point in the X-Y Plane that does Not lie on the X-Axis depicted in Figures (1) and (2), p = c cos θ; and q = c cos Ф Therefore, from the Generalized Equation, a = 1 We get the value of Lorentz Factor, a in this special case as follows: Substituting the expression for a given by Equation (T5) in the Equations (T3) and (T4), we get the Generalized Transformation Equation for Space Difference as follows: The above Equations may be written in the following format to make explicit the fact that the two Equations are identical: x' For the particular case p = q = ± c, The above is the pure form Lorentz Transformation Equation for Space Difference.
The fact that the above Equations are identical is very much apparent on the face of them.
There is no intertwining of Space and Time.

We can derive the Generalized Lorentz Transformation Equation for Time
Difference as follows: Similarly, it can be shown t = = a(q/p) (t' + vx'/q 2 )

which is the Inverse Lorentz Transformation Equation for
Time Difference.
Therefore, Lorentz Transformation is valid only if x' = ct' when x = ct.
Thus, we have disproved in three ways Einstein's claim that the equation € 2 + ή 2 + ζ 2 = c 2 τ 2 represents a spherical wave with velocity of propagation c when viewed in the moving system. In fact, the equation represents only a one-dimensional wave propagating in the direction of the relative velocity between the two systems.
It is relevant to note that Einstein's derivation of Lorentz Transformation Equations itself was regarding a ray of light transmitted along the X-axis. "From the origin of system k let a ray be emitted at the time τ0 along the X-axis to x'," [2]. His assumption in a later part of his paper that Lorentz Transformation Equations so derived by him were valid even for the events of the light wave reaching the spatial points not lying on the Xaxis has been proved to be wrong in the above-detailed discussion.

PART -II
Moving clocks run slow? 2.2.1 "Moving Clocks run slow" is not at all a prediction of Lorentz Transformation.
Lorentz Transformation compares the space and time intervals between two events measured in one inertial frame with those measured in another frame. If t' < t, it does not mean that the clock in the primed frame run slower than the one in the unprimed frame.
The perfect functioning of the measuring tools is a basic premise of any Transformation, Lorentz Transformation not excluded. That t' < t only means that the time interval between the two events measured in the primed frame is shorter than that measured in the unprimed frame.
In the following discussion, we shall follow the convention of defining an event by (x,t) where x and t refer to space and time coordinate of the event. When Lorentz Transformation is applied to two events, it is usual, for the simplicity of mathematical operations, to define the first event as (0,0) in both frames and the second event by (x,t) in one frame, say S, and (x',t') in the other frame, say S', so that x and x' give the space difference and t and t' the time difference between the two events in the frames S and S' respectively.
If an instant of time is shown as t by one clock, and the same instant of time as t' by another clock and t' < t, then we can say that the second clock runs slower than the first clock. But, when t' is really an earlier instant of time shown by that clock at that instant of time, it does not mean that the clock runs slow.
In this section we are going to prove in three methods that when Lorentz Transformation says t ≠ t', it does not mean that the moving clock runs slower than the stationary clock and it only means that t and t' are two different instants in the Absolute Time Chain.

FIRST METHOD -MUTUAL LENGTH CONTRACTION
When Jill is shorter than Jack, it means Jack is taller than Jill. But, according to Lorentz Transformation, when two rods of equal length are in motion with a uniform, linear, relative velocity between them, an observer on one rod would find the other rod shorter than his rod, and vice versa. Lorentz Transformation makes this seemingly impossible feat possible only because of its stand that when the time instant of happening of an event is t in one frame and t' in another frame, t and t' do not denote one single moment, but they are two different instants in the Absolute Time Chain Let two rods, say AB and A'B' of equal length L, while both are at rest, are in motion with a uniform, linear, relative velocity, say v. When the ends A and A' coincide, let the observers set the clocks at those ends to read 0.  Obviously, the light wave would reach the two ends A' and B' simultaneously in the train frame. But, according to Lorentz Transformation, from the viewpoint of a stationary observer on the platform, the light wave would reach the two ends at two different instants of time. An event is absolute in the sense that the observers in all inertial frames would agree that it has happened, but they differ on only when it happened. If t and t' were only different labels of the same instant of time, then Einstein's claim that "Simultaneity is relative" would be meaningless.

THIRD METHOD -LENGTH CONTRACTION
Let A and B be two points on Earth with a distance D between them. From the perspective of any stationary observer on Earth, a particle, say P, moving with a velocity of v would move from A to B in D/v seconds. The time of travel t = D/v Since the Earth Frame is the moving frame from the perspective of P Frame, the distance D between the points A and B on Earth would be a shortened distance D/a for that frame. Therefore, from the perspective of P Frame, the shortened distance D/a will be covered by the particle P, moving with a velocity of v in D/av seconds. The time of travel t' = D/av Therefore t' < t was not due to the moving clock going slow, but it was because the distance was covered in a shorter time from the perspective of the frame of the particle that covered the distance.

The same event recurs infinite times
When a specific event is represented by (X, T) in the frame S, for that frame, it had happened when the Time was T. For any other frame moving with a velocity v relative to it, the same event has occurred at the time t' given by the following expression.
Since the value of v is different for different frames, it varies between -∞ to + ∞. So, the event repeats infinite times -one instance for each inertial frame.
According to Lorentz Transformation, every event in the universe happens at different times for different inertial frames, which implies that the same event recurs infinite times.
The following Graph depicts how simultaneous events observed in one frame are not simultaneous in another frame.
The simultaneous events happening at different instants of time in the perspective of an inertial frame of reference along the X-axis have been shown as horizontal lines in the graph. Each horizontal line corresponds to a line inclined at the angle tan -1 (-av/c 2 ) to it give the time instants of those events (not simultaneous but spread over an infinite spectrum) from the perspective of another inertial frames. The simultaneous events happening in the entire universe at an instant of time t relative to an observer in any inertial frame spread over an infinite time spectrum for the observers in all other frames.

2.2.6
The observed slowing down of moving clocks may be due to Relativistic Variations of mass with velocity and gravity with altitude.
The observed slowing down of clocks moving with a high-speed relative to the Earth has to be traced to some reason other than Lorentz Transformation. It may be examined whether it is due to the period of oscillation of the clock getting changed on account of PART -III An explanation for the constancy of the Speed of Light in all inertial frames, based on Perceptional Relativity

Basic Premises
The following two premises underline the whole gamut of Physics.

The Laws of Physics have been discovered and derived from an observer's
perspective while that observer rests in an inertial frame of reference.

Space is at rest relative to the observer's Frame of reference, and all other
inertial frames are moving in that Space.
The second premise ensures the certainty of measurements of the distances in Space travelled by the moving objects, which is not guaranteed when Space also is moving relative to the observer.

Space is stationary in every Frame.
Space is static in his Frame for any observer, and the other frames move in that Space.
Just like there is a common perception of the stationary observers in every Frame that their Frame alone is at rest while all other frames are moving, those observers share another common perception that Space is at rest in their Frame. Since an observer observes that the objects attached to his Frame are at rest and Space is static, he assumes that Space is also linked to his reference frame. This perception implies that any Point in Space can be claimed to be attached to his Frame of reference by any observer regardless of his motion relative to other observers.
Let an observer stationed in an inertial frame, say S, places a minuscule material marker p at a spatial point to identify that point. An observer stationed in another inertial frame, say S', which moves at a speed v m/s relative to the frame S, also places a minuscule material marker q at another spatial point to identify that point. Let the distance between the markers p and q be v meters at one instant of time. After 1 second, the two markers would collide. That spatial point of the happening of the event of collision would be the point p from the perspective of the observers of the frame S; it would be the point q from the perspective of the observers of the frame S'. Light's starting point. Obviously, that marker will remain stationary in his Frame. An observer in another frame of reference can also place another marker, say O', at the same point, and that marker will remain stationary in that Frame. There will undoubtedly be relative displacement between the two markers after that instant of time. Still, each observer will assume that his marker has remained at the Same point in Space while the other marker has been moving. Thus, every observer can claim that the light source is stationary in and attached to his Frame.

An observer detects Light using a Light
Detector that is at rest in his Frame alone.
Any Light Detector, any material object for that matter, is at rest in only one inertial Frame, and it is moving relative to all other frames. In fine, for any detection of Light by any observer, he has to ensure that both the Light Source and the Light Detector are attached to his Frame of Reference.

For any observer, Light spreads in his Frame alone.
There is an infinite number of inertial frames of referenceeach Frame moving with a non-zero velocity relative to any other frame. When a spherical electromagnetic wave propagates with a speed c from a Space point in all directions, it spreads in each of the infinite inertial frames of reference. But, for an observer in any one of those frames, his perceived facts are the following: beyond his perception and hence of no concern to him.
Suppose the velocity of a moving material particle (i.e., a particle having mass) relative to a frame of reference is known. In that case, to calculate the particle's velocity relative to   Any Light Detector can detect Light originating from a light source that is at rest in the same Frame in which it is also at rest. It follows that no static observer in an inertial frame detects Light that has originated from a Light Source that is not at rest relative to his Frame. To make this fact amply clear, we may adopt the following statement as the Third Postulate of the Special Theory of Relativity (STR) in place of Lorentz Transformation, a suggestion given by this author in an earlier paper under the title "An implicit and untested premises of the Special Theory of Relativity" [5] "The detection of light by an inertial reference frame is an event that is exclusive to that frame." The above statement implies that the Speed of Light relative to any inertial reference frame cannot be measured by any observer who is not stationary in that Frame. The Constancy of the Speed of Light measured in all frames of references is due to each observer's perceptions that Space is at rest relative to his Frame of Reference, and the light source and the light Detector are static in his Frame of reference.
Space is the medium for the transmission of electromagnetic waves. The speed of the propagation of electromagnetic waves relative to Space is c, a constant. Since Space is at rest in any inertial frame of reference, the speed of the transmission of electromagnetic waves relative to any inertial frame of reference is also c. Thus, we have derived a precise explanation for the Speed of Light's constancy measured in all frames of references without 'torturing' the observers' measuring rods and clocks.
PART -IV

Mass -Energy Equivalence
Suppose the mass of a particle when it is at rest in an inertial frame is m 0 . Let its relativistic mass be m, while it is moving with speed v relative to that Frame. We know 1. It has been experimentally proved that no particle can travel faster than c, the Speed of Light. When a particle's speed is accelerated to a value near c, the inertial mass m that resists acceleration tends to become ∞, thereby making it impossible to make the particle reach Light's speed. As already said, the observed slowing down of clocks moving with a high-speed relative to the Earth in Hafele-Keating experiment may be due to the variation of the mass of the clock with its velocity.

The above equation corresponds
It has been shown in many textbooks [7] on Special Theory of Relativity that from the above equation giving a variation of mass with velocity, the following famous massenergy equivalence equation can be derived;

E = mc 2
Thus, Mass-Energy Equivalence can be derived without Lorentz Transformation, Section 3: Conclusions 1. The Constancy of the Speed of Light measured in all frames of references is due to each observer's perceptions that Space is at rest relative to his Frame of Reference, the Light Source is static in his Frame of Reference, the Light originating from that stationary Source spreads as a spherical electromagnetic wave in all directions with a speed c in his static Space; and the Light so spreading is capable of being detected only by any Light Detector that is stationary in the Frame.
2. The detection of Light by an inertial reference frame is an event that is exclusive to that Frame.

Lorentz Transformation is conceptually flawed.
4. Time is absolute. There is no Interdependence of Space and Time.